Finite Group DatabasebetaFinite Group Databasebeta| order | 972 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C3 |
No aliases for this group.
| derived | C3×H(3,𝔽3) ⋊ C3×C4 |
| Sylow | #6856 ⋊ C4 |
113 conjugacy classes of subgroups.
| transitive degree | μt(G) = 108 |
Polycyclic presentation:
2,3,2,3^4|a^2=c,d^a=d^2,e^a=e^2g,f^a=f^2,d^b=de,e^b=ef,e^d=eg62 conjugacy classes — view the full character table.
| maximal subgroup of | #14515720, #92159⋊C4, #14515724, … |
| maximal normal subgroup of | #14515720, #92159⋊C4, #14515724, … |
| maximal quotient of | #14515619, C2×#11757282 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(972, 7);